Theorem lttrii

Description: 'Less than' is transitive. (Contributed by SN, 26-Aug-2025)

	Ref	Expression
Hypotheses	lttrii.a	|- A e. RR
	lttrii.b	|- B e. RR
	lttrii.c	|- C e. RR
	lttrii.1	|- A < B
	lttrii.2	|- B < C
Assertion	lttrii	|- A < C

Proof

Step	Hyp	Ref	Expression
1		lttrii.a	|- A e. RR
2		lttrii.b	|- B e. RR
3		lttrii.c	|- C e. RR
4		lttrii.1	|- A < B
5		lttrii.2	|- B < C
6	1 2 3	lttri	|- ( ( A < B /\ B < C ) -> A < C )
7	4 5 6	mp2an	|- A < C